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Chapter 8
Endoscope Optics
Endoscopes are used to observe otherwise inaccessible areas within the human
body either noninvasively or minimally invasively. Endoscopes have
unparalleled ability to visualize lesions within internal organs with high
resolution through natural body orifices, such as the mouth, nose, anus, and
urethra. With high-resolution endoscopes, harvesting biopsy samples for later
laboratory analysis may not be necessary.
The history and basic optics of endoscopes will be discussed in Secs. 8.1 and
8.2. Sections 8.3, 8.4, and 8.5 will discuss the optics and optical design of relay
lenses, objective lenses, and illumination systems. Section 8.6 will focus on the
imaging and illumination systems of wireless endoscopes.
8.1 Introduction
The earliest endoscope-using lens was called the cystoscope. It was invented by
Maximilian Nitze in 1877 and was used to examine the interior of the urinary
bladder through the urethra.1 In 1932, G. Wolf introduced the first semiflexible
gastroscope, and in 1956, Basil Hirschowitz performed the first image
transmission with fiber bundles. In 1959, Harold H. Hopkins invented rod lenses
for image transmission, and in 1963, Karl Storz combined rod lenses for image
transmission with fiber bundles for illumination.2 A video endoscope with a
camera on the eyepiece was first introduced in 1987, and a video endoscope with
a camera at the distal end of the endoscope was demonstrated in 1992.1 In the late
1990s, with the advances in light sources, sensors, and electronics, a wireless
endoscope was invented for small-bowel imaging.3
Traditional endoscopes comprise an airtight and waterproof elongated tube
having a distal end with an objective lens for imaging and a proximal end with an
eyepiece for viewing. The elongated tube includes a relay lens system, or a fiber
bundle, to transmit the image formed by the objective lens to the proximal end of
the tube. The function of the eyepiece is to magnify the image at the proximal
end for the observer. Endoscopes used in clinical applications further consist of a
work channel and an irrigation channel.
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In the last five decades, the introduction of optical fibers, rod lenses, and then
the electronic detector has advanced the development of endoscopes
dramatically. Various endoscopes have been developed for general applications
and to meet some special requirements. Some commonly used endoscopes are:





Arthroscopes to examine joints,
Bronchoscopes to examine air passages and lungs,
Colonoscopes to examine the colon,
Cystoscopes to examine the urinary bladder,
Gastroscopes to examine the small intestine, stomach, and esophagus,
and
 Hysteroscopes to examine the uterus.
8.2 Basic Optics for Endoscopes
In some form or another, all endoscopes use optical elements to guide light to a
target and transfer an image to the eye or to a detector. The basic optical elements
of an endoscope include an illumination system, an imaging system, an image
transmission system (relay system), and a viewing system (eyepiece or electronic
sensor).
Figure 8.1 is a diagram of a conventional optical system in a rigid endoscope
where, for simplicity, only one relay stage is shown. The system consists of three
basic and separate optical components, as follows:

y1
yn
E
O

yo
Objective
lens
Relay lens
Eyepiece
Figure 8.1 Typical optical layout of a conventional endoscope with a one-stage
relay lens. It consists of three lenses: the objective lens, relay lens, and
eyepiece. Here yo is the height of the field, y1 is the first intermediate image
height, and yn is the final image height through the relay lens. E is the exit pupil of
the eyepiece, and it is the location for placement of the observer’s pupil.
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 An objective lens, which forms the first inverted intermediate image y1
of the object yo.
 A relay lens system, which reimages the first intermediate image y1 to
the final image yn at the proximal end of the endoscopic tube. In most
endoscopes, there are several unit-magnification relay lenses forming
the intermediate images y2, y3, …, and the final image yn.
 An eyepiece or a focusing lens, which presents the final image yn to a
sensor. Traditionally, an eyepiece is attached to the endoscope and
produces a magnified virtual image for the observer. In modern
endoscopes, a camera lens is attached to the endoscope, and it produces
a real image on the electronic sensor. The image is then displayed on a
monitor or other display device.
According to optical transmission systems, we can classify endoscopes into
three groups: rigid, fiber optic, and video. In recent years, some new types of
endoscopes, such as wireless, scanning, and stereo endoscopes, have been
developed.
8.2.1 Illumination and imaging optics
Figure 8.2 illustrates a basic optical configuration at the distal end of an
endoscope. The light from the fiber bundle illuminates the observation region.
Part of the reflected light from the tissue is captured by the objective lens.
There are two major obstacles to designing an endoscope having a small
diameter. The first obstacle is the lack of sufficient illumination. An endoscope
with a small diameter does not provide enough space to transmit light. The
second obstacle is light collection efficiency. The aperture is small because of the
small diameter of the endoscope, which results in a low light collection
efficiency.
The amount of light captured by the eye or an electronic sensor is principally
determined by three factors:



The intensity of the light incident upon the observation region,
The optical characteristics of the observation surface, such as surface
reflectivity and curvature, and
The light collection efficiency of the objective lens and the transmission
of the optical system.
The brightness of the image seen in an endoscope depends on the level of
illumination falling on the region being viewed, as discussed below.2
The total amount of light captured by the endoscope from a uniformly diffuse
reflecting surface is given by
  LR (yo2 )( sin 2 ) ,
(8.1)
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Fiber bundle
yo


p
z
Fiber bundle
Figure 8.2 Basic optical configuration at the distal end of an endoscope. The
light from the fiber bundle illuminates the tissue. Part of the reflected light is
captured by the objective lens.
where L is the radiance from the fiber bundle, R is the reflection coefficient, yo is
the object height, and yo2 is the area of the object, assuming that the FOV is
circular, α is the cone angle of the light accepted by the objective lens, and πsin2α
measures the on-axis solid angle of the cone of rays accepted by the endoscope.
All of the parameters are shown in Figs. 8.1 and 8.2.
The cone angle α of the light accepted by objective lens is approximately
determined by the radius p of the entrance pupil of the objective lens and the
working distance z:
sin  
p
.
z
(8.2)
Therefore, Eq. (8.1) becomes
2
 p
   LRy   .
z
2
2
o
(8.3)
The total amount of light accepted by the endoscope is proportional to the
radiance L and inversely proportional to the square of the working distance z.
In object space, the optical invariant is defined as
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383
H  n sin() yo ,
(8.4)
where n is the refractive index of the medium in object space. Equation (8.1)
becomes

2 LR 2
H
n2
(8.5)
for the given illumination and the object distance. The total amount of light
entering the endoscope is proportional to H 2.
8.2.2 Rigid endoscopes
As the name suggests, rigid endoscopes have a rigid tube to house the refractive
relay lenses and illumination fibers. The relay lenses transfer the image at the
distal end to the proximal end of the tube so that the image can be directly
viewed through an eyepiece or with an imaging detector. When the endoscope is
designed for direct view through the eyepiece, an odd number of relay stages is
required in order to correct for the inversion produced by the object because the
eyepiece has a positive magnification and does not produce an inverted virtual
image. When an electronic sensor is used in an endoscope, the parity of the
number of relay stages is not important since the inversion can always be
performed electronically or through software.
As seen from Fig. 8.1, the relay system determines the value of the optical
invariant H of the entire imaging system. In object space, the optical invariant is
determined by Eq. (8.4). While in the plane of the entrance pupil, the optical
invariant is
H  n sin() p ,
(8.6)
where β is the field angle and p is the radius of the entrance pupil, as shown in
Fig. 8.2.
Given the H of the relay system and the FOV, either the object height yo or
the field angle β and the semiangle of the on-axis marginal ray α or the radius of
the entrance pupil p can be obtained from Eqs. (8.4) and (8.6). Once the FOV is
determined, the size of the relay system governs the focal length f of the
objective lens by
f tan   r ,
(8.7)
where r is the radius of the clear aperture of the relay lens.
The depth of field of the rigid endoscope is determined by the viewing
configuration. When an eyepiece is mounted at the proximal end of the
endoscope, the accommodation of the human eye helps to extend the DOF. The
normal human eye can focus from infinity to a near point, which is 250 mm from
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the eye. Therefore, the depth of field is calculated by the difference between two
working distances: the working distance of the objective lens when the final
image is located 250 mm from the exit pupil of the eyepiece and the working
distance when the image is at infinity.
When a CCD or CMOS sensor is used at the proximal end of an endoscope,
the depth of field is smaller than that of an endoscope using an eyepiece. The
depth of focus can be calculated from the requirement of the resolution and the
size of the pixels in the CCD or CMOS sensor, as discussed in Chapter 2.
One special requirement for objective lenses used in rigid endoscopes is the
telecentricity that prevents light loss during image transmission from the distal
end to the proximal end. As shown in Fig. 8.3(a), when the objective lens is not
telecentric, the off-axis ray may miss the relay lens, for example, ray 1, or it
cannot be transferred to the next intermediate image plane, such as ray 2, because
it hits the edge of the relay lens. The ray may be absorbed by the lens edge or
may be reflected back to the relay lens. Generally, rays reflected from the edge of
the relay lens degrade image quality and should be minimized. The objective lens
1
2
Objective lens
Relay lens
(a)
Objective lens
Relay lens
(b)
Figure 8.3 (a) Ray diagram of a nontelecentric objective lens. Rays 1 and 2
cannot be relayed to the next intermediate image. (b) Ray diagram of a
telecentric objective lens. All of the rays are relayed to the next intermediate
image.
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in Fig. 8.3(b) is telecentric in the image space where the chief ray is parallel to
the optical axis. All of the off-axis rays enter the relay lens and can be transferred
to the next intermediate image.
There are three types of relay systems used in rigid endoscopes, namely,
traditional lenses, rod lenses, and GRIN lenses. Section 8.3 will discuss the
properties and design of each relay system.
8.2.3 Flexible endoscopes
Flexible endoscopes use imaging fiber bundles to transfer the image from the
distal end of the endoscope to the imaging lens or eyepiece, as shown in Fig. 8.4.
With fiber bundles, the diameter of the space required for the image relay is
reduced significantly, leaving more space for other instrument channels. Other
advantages of fiber-optic endoscopes include transmitting the image over long
distances and observing around corners.
An imaging fiber bundle typically contains about 3000 or more optical fibers
packed into a hexagonal array. The spatial arrangement of the fibers at both ends
is identical, enabling a spatially coherent transmission of the image. The optical
fibers are multimode and preserve the color of light. The core diameter is
typically 3 µm, the overall diameter of the imaging bundle varies between
0.2 and 3 mm, and the fiber bundle may be over 2 m in length.
The resolution of a flexible endoscope is limited by the core diameter of the
fiber bundle. Because of the pixelated nature of the fiber bundle, flexible
endoscopes have a smaller depth of field than the conventional endoscopes with
refractive relay lenses. The calculation of the depth of field is discussed in detail
in Chapter 3. The telecentricity of the objective lens on the fiber side is required
in order to couple more light into and out of the fiber bundle.
Unlike endoscopes with refractive relay lenses, where the eyepiece can be
designed to compensate for the residual aberrations accumulated from the
objective and relay lenses, the eyepiece in fiber endoscopes can only give a sharp
image of what appears at the proximal end of the fiber bundle, and it cannot
Fiber bundle for
illumination
Fiber bundle for
image relay
A'
O'
A
O
Objective lens
Fiber bundle for
illumination
Eyepiece or
imaging lens
Figure 8.4 Optical layout of a typical fiber-optic endoscope.
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correct the blur of the image formed at the distal end by the objective lens and
transmitted by the fiber bundle.
8.2.4 Video endoscopes
One of the most important advances in endoscopes is the introduction of videochip technology on the distal end of the device. Image relay is not necessary
given that the objective lens images the observation surface directly to the
sensing elements in the imaging detector. As shown in Fig. 8.5, the imaging head
of a video endoscope generally consists of an imaging detector, objective lens,
and illumination optics. Two types of imaging detectors, CCD and CMOS, are
commonly used in video endoscopes.
Video endoscopes have revolutionized many surgical procedures by
improving visualization while minimizing the tissue damage that is generally
caused by invasive approaches. The advantages of a video endoscope over a
fiber-optic endoscope include:


The number of pixels in an imaging detector is typically greater than
the number of fibers in a fiber bundle, giving a sharper image.
In a conventional fiber-optic endoscope, the hexagonal sampling,
which is due to the arrangement of the fibers, is followed by a
rectangular sampling through the imaging detector. The mismatch
between these two sequential sampling operations makes processing
fiber-optic endoscope images difficult.
The objective lens of a video endoscope must have a short structural length, a
small diameter, and a wide field angle. Compared to objective lenses used in
rigid and flexible endoscopes, telecentricity is not a requirement for lenses in
video endoscopes, even if it is desired to obtain uniform QE across the field of
view. The incident angle of the chief ray on the image surface increases in
proportion to the field. The chief ray angle should be smaller than the
specification of the imaging detector for a reasonable QE.
Illumination fibers
Window
Figure 8.5 Optical layout of a video endoscope.
Sensor